The number 1609
1609 is a twin prime (1607 and 1609 are both prime) and the 254th prime number. Its only divisors are 1 and 1609.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1609: a twin prime (1607 and 1609 are both prime); the 254th prime number.
- 2
1609 is prime, so its only factors are 1 and 1609. It is the 254th prime; the next prime is 1613 and the one before is 1607.
- 3
The divisors add up to 1610; without 1609 itself that is 1, so 1609 is deficient (1 is less than 1609). Euler's totient φ(1609) = 1608 numbers up to 1609 share no factor with it.
- 4
The digits of 1609 add up to 16, and repeating that until one digit is left gives the digital root 7. The Collatz sequence (halve if even, else 3n+1) takes 73 steps to reach 1.
1609 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 1610 |
| Euler totient φ(n) | 1608 |
| Square | 2588881 |
| Cube | 4165509529 |
| Square root | 40.112342 |
| Digit sum / digital root | 16 / 7 |
| Collatz steps to 1 | 73 |
| Scientific notation | 1.609 × |
1609 in other forms
| Form | Value |
|---|---|
| In words | one thousand six hundred and nine |
| Roman numerals | MDCIX |
| Binary (base 2) | 11001001001 |
| Octal (base 8) | 3111 |
| Hexadecimal (base 16) | 649 |
| Base 3 | 2012121 |
| As time | 1609 seconds = 26 min 49 s |
Is 1609 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 1) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 4) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 1) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 6) | A number is divisible by 7 if double the last digit and subtract it from the rest: the result is a multiple of 7. |
| 8 | No (remainder 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 7) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 9) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 3) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 1) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1609 a prime number?
Yes. 1609 is divisible only by 1 and itself.
What are the factors of 1609?
1, 1609.
What is 1609 in binary?
11001001001 (hexadecimal 649, octal 3111).
What is the square root of 1609?
About 40.1123.
What is 1609 in Roman numerals?
MDCIX.
Is 1609 divisible by 3?
No. Its digits add up to 16, which is not a multiple of 3.
What is special about the number 1609?
1609 is a twin prime (1607 and 1609 are both prime); the 254th prime number.